Heather Watson kisses the trophy after winning the Japan Open in Osaka. Photograph: Jiji Press/AFP/Getty Images

A lot of history has been made in British tennis lately and on Sunday Heather Watson added her name to the list when she became the first woman from these shores to win a WTA Tour title since 1988 with her victory in the Japan Open in Osaka. After Andy Murray's triumphs at the Olympics and the US Open, where he broke a 76-year men's grand slam drought, Watson snapped a 24-year winless streak by beating Chang Kai-chen of Taiwan 7-5, 5-7, 7-6 for the first of what promises to be many titles to come.

"I was in the changing room afterwards, changing my clothes, and I thought to myself, 'Did I really win?,'" said the 20-year-old, who won $37,000 (£23,000) and is set to break into the world's top 50 for the first time on Monday. "It's just starting to settle in. I'm proud to do it for my country and to represent them. Recently, we've been breaking quite a lot of records so I'm happy I could break another one today and hopefully I can break some more."

Three weeks ago, the 18-year-old Briton Laura Robson almost pipped her to the post when she reached the final in Guangzhou, China, only to fall in three sets. Watson looked to be heading the same way when Chang served for the match in the third set but she dug deep to save four match points and then clinched victory in a nail-biting final-set tiebreak after three hours, 11 minutes. "I've worked so, so hard for this moment, throughout my career," Watson said. "That's why I ran all those miles and lifted all those weights, for moments like this."

Born and raised in Guernsey, Watson has trained in the United States, at the Nick Bollettieri academy, since she was 12, part-funded by the Lawn Tennis Association. Bollettieri was the man responsible for discovering Andre Agassi, Maria Sharapova, Monica Seles and Anna Kournikova and Watson is another success story for the American.

Watson and Robson are seen as the future of women's tennis in Britain and the LTA must be hoping that the two players, good friends off the court, could lead to a surge in girls playing the sport, helped not only by their tennis but their outgoing personalities, too. "I didn't think about that but I'd like to inspire the younger generation to play tennis and to follow their dreams and work hard," Watson said. "I think I can do that through my tennis by achieving things and showing them that anything's possible."

Watson will leapfrog Robson in the rankings on Monday , at No50 to Robson's 52, and the pair are well placed to head towards the top 20 next year. Robson, who does not turn 19 until January, reached the fourth round of the US Open while Watson made the third round at Wimbledon this summer.

The bookmakers are already taking bets on who will be higher in the rankings next year and Watson says their friendly rivalry – they appeared together in a Gangnam-style video with fellow players last week that has gone viral on YouTube – is spurring each of them on to bigger and better things. "Knowing Laura did so well in China a few weeks ago definitely motivated me this week," Watson said. "But it's great we're really good friends off the court as well."

While Watson came out on top after an epic battle, Murray was unable to make it a double celebration when he was edged out 5-7, 7-6, 6-3 by Novak Djokovic in the final of the Shanghai Masters on Sunday. The world No3 Murray had five match points in the second-set tiebreak but Djokovic survived and clinched victory after three hours, 21 minutes, a small measure of revenge for his defeat by the Scot in the US Open final last month. "It's a disappointing one to lose," Murray said. "But I'm sure I'll recover from it pretty well."